Sphere

A sphere is a three-dimensional object that is perfectly round, just like a ball. It is defined as the set of all points in space that are at a given distance (radius) from a given point (center). The distance from the center to any point on the sphere is constant.

Formulas for a Sphere

The following are the key formulas for a sphere:

• Surface Area: The surface area (A) of a sphere with radius (r) is given by the formula: A = 4πr²
• Volume: The volume (V) of a sphere with radius (r) is given by the formula: V = (4/3)πr³

Surface Area of a Sphere

The surface area of a sphere is the total area on the outside of the sphere. To find the surface area of a sphere, you can use the formula A = 4πr², where r is the radius of the sphere.

Volume of a Sphere

The volume of a sphere is the amount of space inside the sphere. To find the volume of a sphere, you can use the formula V = (4/3)πr³, where r is the radius of the sphere.

Practice Problems

1. Find the surface area of a sphere with radius 5 units.
2. Find the volume of a sphere with radius 3 units.
3. A sphere has a surface area of 154π square units. Find its radius.
4. A sphere has a volume of 36π cubic units. Find its radius.

Make sure to practice solving problems using the formulas for surface area and volume of a sphere to solidify your understanding of this topic.

Real-World Applications

Spheres are commonly found in real-world objects such as balls, planets, and bubbles. Understanding the properties of spheres and how to calculate their surface area and volume can be useful in fields such as architecture, engineering, and physics.

Remember to use the formulas and practice problems to become comfortable with working with spheres. Good luck!